Question

Q7 Q30.) Find the area of the triangle specified below.

Answer 1

Use Heron's formula to find the area of the triangle since you're given all the side lengths.

Heron's formula:
`√(s(s-a)(s-b)(s-c))`, where s =
`(a + b + c)/(2)`.

Find s.

`(19 + 21 + 15)/(2)` = 27.5

Now plug in s and a, b, and c into the formula.


`√(27.5(27.5-19)(27.5 - 21)(27.5 - 15))` = 137.8

The area of the triangle is 138 square meters.

Answer 2

Let the sides of the triangle be a = 19 m, b = 21 m, c = 15 m


`p = (a + b + c)/(2)`

`p = (19 + 21 + 15)/(2)`

`p = (40 + 15)/(2)`

`p = (55)/(2)`

`p = 27.50`

By Heron's Formula, area of triangle

`s = √(p * (p - a) * (p - b)* (p - c))`

`s = √(27.50 * (27.50 - 19) * (27.50 - 21) * (27.50 - 15))`

`s = √(27.50 * 8.50 * 6.50 * 12.50)`

`s = √(233.75 * 6.50 * 12.50)`

`s = √(1519.38 * 12.50)`

`s = √(18992.25)`

`s = 137.81`

`A = 138 \: (rounded \: to \: the \: nearest \: integer)`